The natural frequency or pitch of a taut string, or taught strings is defined by the following equation f=(1/L).sqroot.(T/M)
where:
T=Tension in Strings PA1 f=Frequency of Vibration PA1 M=Mass Density of Strings PA1 L=Length of Strings
Conversely, if the frequency is known, other things being equal, the tension may be determined.
The above equation may be utilized to determine, for instance, the tension, or of a tennis racket. The structure of the strings in a tennis racket essentially involves strings of equal tension, fixed mass per given length, and varying string lengths. The strings are usually of nylon or synthetic gut polymer composition, having a diameter from 15 to 17 gauge (1.38 mm to 1.22 mm); usually 16 gauge (1.30 mm). Current-day adult rackets are wound with areas varying from roughly 90 to 125 square inches playing area, with the vast majority (95%) being from 95 to 115 square inches in playing area.
For a given string size and mass, and given racket model, the tension varies as the square-root of the natural frequency of the racket. Once the natural frequency is determined, the string tension, in pounds, can be determined. Other factors will have an effect, such as the string size and mass, but for a given string size and mass a close approximation to the racket tension can be determined from the natural frequency of the racket.